Question: $ E = \left[\begin{array}{rrr}3 & 3 & -1 \\ -1 & 0 & -2 \\ -1 & -2 & 0\end{array}\right]$ $ B = \left[\begin{array}{rrr}0 & -1 & 3 \\ 1 & 1 & -1 \\ 1 & 0 & 0\end{array}\right]$ Is $ E- B$ defined?
Explanation: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ E$ is of dimension $( m \times  n)$ and $ B$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ E$ ) must equal $ p$ (number of rows in $ B$ ) and 2. $ n$ (number of columns in $ E$ ) must equal $ q$ (number of columns in $ B$ Do $ E$ and $ B$ have the same number of rows? Yes Yes No Yes Do $ E$ and $ B$ have the same number of columns? Yes Yes No Yes Since $ E$ has the same dimensions $(3\times3)$ as $ B$ $(3\times3)$, $ E- B$ is defined.